I opened your file in M8 and evaluated the notebook. It ran rapidly until the line in input 17 that reads:
riem = ered[
Table[D[gam[[i, j, l]], co[[k]]] - D[gam[[i, j, k]], co[[l]]] +
Sum[gam[[i, p, k]] gam[[p, j, l]] -
gam[[i, p, l]] gam[[p, j, k]], {p, 4}], {i, 4}, {j, 4}, {k,
4}, {l, 4}]];
That line generated four errors:
Part::partd: Part specification gam[[1,1,1]] is longer than depth of object. >>
Part::partd: Part specification co[[1]] is longer than depth of object. >>
Part::partd: Part specification gam[[1,1,1]] is longer than depth of object. >>
General::stop: Further output of Part::partd will be suppressed during this calculation. >>
After that it just kept running and I aborted the rest.
M9 hangs up at the same spot.